About Factoring Trinomials Part 1:
When we factor a trinomial with a leading coefficient of 1, we reverse the FOIL process. Write two sets of parentheses and start with the first spots: if we see x2, we know that is produced by x • x. We then find the last positions from two integers whose sum is b and whose product is c.
Test Objectives
- Demonstrate the ability to factor out the GCF from a trinomial
- Demonstrate the ability to find two integers whose sum is b and whose product is c
- Demonstrate the ability to factor a trinomial into the product of two binomials
- Demonstrate the ability to factor a trinomial when two variables are involved
#1:
Instructions: Factor each.
a) $$v^2 + 11v + 30$$
b) $$x^2 - 3x - 4$$
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#2:
Instructions: Factor each.
a) $$x^2 - 4x - 28$$
b) $$x^2 + 15x + 44$$
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#3:
Instructions: Factor each.
a) $$2x^2 + 16x + 24$$
b) $$3m^2 - 18m - 81$$
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#4:
Instructions: Factor each.
a) $$2x^2 + 14xy - 36y^2$$
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#5:
Instructions: Factor each.
a) $$6x^2 + 36xy + 30y^2$$
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Written Solutions:
#1:
Solutions:
a) $$(v + 5)(v + 6)$$
b) $$(x - 4)(x + 1)$$
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#2:
Solutions:
a) $$\text{Prime Polynomial}$$
b) $$(x + 4)(x + 11)$$
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#3:
Solutions:
a) $$2(x + 6)(x + 2)$$
b) $$3(m + 3)(m - 9)$$
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#4:
Solutions:
a) $$2(x + 9y)(x - 2y)$$
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#5:
Solutions:
a) $$6(x + 5y)(x + y)$$
